Solve for $k$, $ \dfrac{6}{10k - 15} = -\dfrac{2}{8k - 12} - \dfrac{k - 9}{2k - 3} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10k - 15$ $8k - 12$ and $2k - 3$ The common denominator is $40k - 60$ To get $40k - 60$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{6}{10k - 15} \times \dfrac{4}{4} = \dfrac{24}{40k - 60} $ To get $40k - 60$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{2}{8k - 12} \times \dfrac{5}{5} = -\dfrac{10}{40k - 60} $ To get $40k - 60$ in the denominator of the third term, multiply it by $\frac{20}{20}$ $ -\dfrac{k - 9}{2k - 3} \times \dfrac{20}{20} = -\dfrac{20k - 180}{40k - 60} $ This give us: $ \dfrac{24}{40k - 60} = -\dfrac{10}{40k - 60} - \dfrac{20k - 180}{40k - 60} $ If we multiply both sides of the equation by $40k - 60$ , we get: $ 24 = -10 - 20k + 180$ $ 24 = -20k + 170$ $ -146 = -20k $ $ k = \dfrac{73}{10}$